Title: Frequency domain analysis for structural breaks of non-stationary spatial data
Authors: Weiyu Zhou - George Mason University (United States) [presenting]
Pramita Bagchi - George Mason University (United States)
Abstract: Appropriate modelling of the second-order structure is of prime importance in spatial data analysis. A commonly used assumption for modelling spatial covariance is the assumption of second-order stationarity. However, this assumption is often violated in practice, and its misspecification can lead to a wrong inference. We propose to develop a methodology to test the assumption of stationarity in spatial data and identify stationary (or approximately stationary) sub-regions. We define a frequency domain based spatial process, which takes a high value near any location with second-order change in the underlying random field. We propose a consistent estimator of the aforementioned spatial process based on a partial observation of the random field.We establish the asymptotic convergence of a centered and scaled version of this estimator to Gaussian process for a block-wise stationary random field and propose a consistent level $\alpha$ test for stationarity based on the asymptotic distribution based on the simulated quantiles. We also propose an algorithm to identify the different stationary regions for a block-wise stationary random field or regions with similar second-order property for the locally stationary random field.